Starting with GFXbench, the listing reveals a handset carrying the model number SM-J105F, and sporting the Spreadtrum SC8830 chipset with quad-core 1.5GHz CPU; 4.3-inch 800x480 pixel display, 1GB RAM and 8GB of storage. The camera setup features 5MP/VGA snappers and the whole thing is running on Android 5.1.1 Lollipop.
A device with same model number was also listed on Zauba (a website which tracks India's import and export), although with a 4-inch display. We are willing to trust these documents on the screen size as benchmarks often get those wrong. The Zauba listing also revealed a price tag of INR 3,368 (around $50).
Finally, what associates the SM-J105F with the Galaxy J1 mini moniker is some code that can be found on Spreadtrum's own website (see screenshot below).